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  <div class="section" id="numpy-apply-along-axis">
<h1>numpy.apply_along_axis<a class="headerlink" href="#numpy-apply-along-axis" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.apply_along_axis">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">apply_along_axis</code><span class="sig-paren">(</span><em class="sig-param">func1d</em>, <em class="sig-param">axis</em>, <em class="sig-param">arr</em>, <em class="sig-param">*args</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/shape_base.py#L269-L414"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.apply_along_axis" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply a function to 1-D slices along the given axis.</p>
<p>Execute <em class="xref py py-obj">func1d(a, *args)</em> where <em class="xref py py-obj">func1d</em> operates on 1-D arrays and <em class="xref py py-obj">a</em>
is a 1-D slice of <em class="xref py py-obj">arr</em> along <em class="xref py py-obj">axis</em>.</p>
<p>This is equivalent to (but faster than) the following use of <a class="reference internal" href="numpy.ndindex.html#numpy.ndindex" title="numpy.ndindex"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ndindex</span></code></a> and
<a class="reference internal" href="numpy.s_.html#numpy.s_" title="numpy.s_"><code class="xref py py-obj docutils literal notranslate"><span class="pre">s_</span></code></a>, which sets each of <code class="docutils literal notranslate"><span class="pre">ii</span></code>, <code class="docutils literal notranslate"><span class="pre">jj</span></code>, and <code class="docutils literal notranslate"><span class="pre">kk</span></code> to a tuple of indices:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Ni</span><span class="p">,</span> <span class="n">Nk</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="n">axis</span><span class="p">],</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">axis</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span>
<span class="k">for</span> <span class="n">ii</span> <span class="ow">in</span> <span class="n">ndindex</span><span class="p">(</span><span class="n">Ni</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">kk</span> <span class="ow">in</span> <span class="n">ndindex</span><span class="p">(</span><span class="n">Nk</span><span class="p">):</span>
        <span class="n">f</span> <span class="o">=</span> <span class="n">func1d</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">ii</span> <span class="o">+</span> <span class="n">s_</span><span class="p">[:,]</span> <span class="o">+</span> <span class="n">kk</span><span class="p">])</span>
        <span class="n">Nj</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">shape</span>
        <span class="k">for</span> <span class="n">jj</span> <span class="ow">in</span> <span class="n">ndindex</span><span class="p">(</span><span class="n">Nj</span><span class="p">):</span>
            <span class="n">out</span><span class="p">[</span><span class="n">ii</span> <span class="o">+</span> <span class="n">jj</span> <span class="o">+</span> <span class="n">kk</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="n">jj</span><span class="p">]</span>
</pre></div>
</div>
<p>Equivalently, eliminating the inner loop, this can be expressed as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Ni</span><span class="p">,</span> <span class="n">Nk</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="n">axis</span><span class="p">],</span> <span class="n">a</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">axis</span><span class="o">+</span><span class="mi">1</span><span class="p">:]</span>
<span class="k">for</span> <span class="n">ii</span> <span class="ow">in</span> <span class="n">ndindex</span><span class="p">(</span><span class="n">Ni</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">kk</span> <span class="ow">in</span> <span class="n">ndindex</span><span class="p">(</span><span class="n">Nk</span><span class="p">):</span>
        <span class="n">out</span><span class="p">[</span><span class="n">ii</span> <span class="o">+</span> <span class="n">s_</span><span class="p">[</span><span class="o">...</span><span class="p">,]</span> <span class="o">+</span> <span class="n">kk</span><span class="p">]</span> <span class="o">=</span> <span class="n">func1d</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">ii</span> <span class="o">+</span> <span class="n">s_</span><span class="p">[:,]</span> <span class="o">+</span> <span class="n">kk</span><span class="p">])</span>
</pre></div>
</div>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>func1d</strong><span class="classifier">function (M,) -&gt; (Nj…)</span></dt><dd><p>This function should accept 1-D arrays. It is applied to 1-D
slices of <em class="xref py py-obj">arr</em> along the specified axis.</p>
</dd>
<dt><strong>axis</strong><span class="classifier">integer</span></dt><dd><p>Axis along which <em class="xref py py-obj">arr</em> is sliced.</p>
</dd>
<dt><strong>arr</strong><span class="classifier">ndarray (Ni…, M, Nk…)</span></dt><dd><p>Input array.</p>
</dd>
<dt><strong>args</strong><span class="classifier">any</span></dt><dd><p>Additional arguments to <em class="xref py py-obj">func1d</em>.</p>
</dd>
<dt><strong>kwargs</strong><span class="classifier">any</span></dt><dd><p>Additional named arguments to <em class="xref py py-obj">func1d</em>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.9.0.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray  (Ni…, Nj…, Nk…)</span></dt><dd><p>The output array. The shape of <em class="xref py py-obj">out</em> is identical to the shape of
<em class="xref py py-obj">arr</em>, except along the <em class="xref py py-obj">axis</em> dimension. This axis is removed, and
replaced with new dimensions equal to the shape of the return value
of <em class="xref py py-obj">func1d</em>. So if <em class="xref py py-obj">func1d</em> returns a scalar <em class="xref py py-obj">out</em> will have one
fewer dimensions than <em class="xref py py-obj">arr</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.apply_over_axes.html#numpy.apply_over_axes" title="numpy.apply_over_axes"><code class="xref py py-obj docutils literal notranslate"><span class="pre">apply_over_axes</span></code></a></dt><dd><p>Apply a function repeatedly over multiple axes.</p>
</dd>
</dl>
</div>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">my_func</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
<span class="gp">... </span>    <span class="sd">&quot;&quot;&quot;Average first and last element of a 1-D array&quot;&quot;&quot;</span>
<span class="gp">... </span>    <span class="k">return</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="mf">0.5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">9</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span><span class="n">my_func</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">array([4., 5., 6.])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span><span class="n">my_func</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">array([2.,  5.,  8.])</span>
</pre></div>
</div>
<p>For a function that returns a 1D array, the number of dimensions in
<em class="xref py py-obj">outarr</em> is the same as <em class="xref py py-obj">arr</em>.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">8</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">7</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">9</span><span class="p">],</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">6</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span><span class="nb">sorted</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">array([[1, 7, 8],</span>
<span class="go">       [3, 4, 9],</span>
<span class="go">       [2, 5, 6]])</span>
</pre></div>
</div>
<p>For a function that returns a higher dimensional array, those dimensions
are inserted in place of the <em class="xref py py-obj">axis</em> dimension.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">],</span> <span class="p">[</span><span class="mi">7</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">9</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">apply_along_axis</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">array([[[1, 0, 0],</span>
<span class="go">        [0, 2, 0],</span>
<span class="go">        [0, 0, 3]],</span>
<span class="go">       [[4, 0, 0],</span>
<span class="go">        [0, 5, 0],</span>
<span class="go">        [0, 0, 6]],</span>
<span class="go">       [[7, 0, 0],</span>
<span class="go">        [0, 8, 0],</span>
<span class="go">        [0, 0, 9]]])</span>
</pre></div>
</div>
</dd></dl>

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